Two forces of magnitude 15N and 4root2N are acting in the directions 3i-4j and i+j respectively, find the magnitude of the resultant of the two forces.
If we call the two forces u and v, then we have (using unit vectors),
u = 15(3/5i - 4/5j)
v = 4√2(1/√2i + 1/√2j)
so, u+v = 13i-8j
I expect you can find the magnitude of that...